Otto W. Nuttli, James E. Zollweg; The relation between felt area and magnitude for central United States earthquakes. Bulletin of the Seismological Society of America ; 64 (1): 73–85. doi:
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Felt areas of earthquakes in the central United States are known to increase sizeably with small increases in magnitude. In order to establish a quantitative relation between magnitude and felt area, 22 recent earthquakes were studied, resulting in the empirical equation
where ƒ is the logarithm to the base 10 of the felt area in square kilometers. This equation can be used to estimate the magnitude of earthquakes in the central United States for which there are intensity maps but no instrumental data. Furthermore, from the equation one can determine that the limit of perceptibility corresponds to a sustained, hard-rock, vertical-component particle velocity of about 22μ/sec.